As a simulation method for simulating surface topography by processing such as etching or a deposition, utilizing an electronic computer, the String Model is well known (refer to "IEEE Trans. Electron Devices, Vol. ED-26, p 1445" by W. G. Oldham).
FIG. 4 shows, in cross-section, a simulation of surface topography in a case of deposition by String Model. In FIG. 4, reference numeral 1 designates a semiconductor substrate on which a material is deposited. Reference numeral 21 designates a point at the substrate surface. Reference numeral 22 designates a segment of the surface of substrate and also of the surface including the advancing deposition. Reference numeral 23 designates the direction in which the deposition is taking place.
In the String Model, by combining the points 21 and the line segments 22, an arbitrary approximating topography is obtained. When the topography changes dependent on the deposition, the movements of the respective line segments 22 are determined at every time interval .DELTA.t (seconds), and the topography after each interval .DELTA.t is thus predicted. Then, the length of the line segment 22 is adjusted to be appropriate at every time interval .DELTA.t. When the line segments 22 are about to cross each other, the line segments 22 are adjusted so as not to cross. Thus, the line segment or string that comprises the point 21 and the line segment 22 is controlled.
FIG. 5 shows a conceptual view of string control when the deposition is conducted isotropically. The points 24, 25, and 26 constitute a deposition surface at time t.sub.i. The points 24, 25, and 26 are named as point (j-1), point (j), and point (j+1), and the coordinates thereof at time t.sub.i are represented as (i, j-1), (i, j), and (i, j+1), respectively. The point 27 is point (j) at time t.sub.i+1 which is .DELTA.t after time t.sub.i, and its coordinate is represented by (i+1, j). When the deposition velocity 28 from time t.sub.i to time t.sub.i+1 is set as (i, v), the relationship between the point 25 and the point 27 is, EQU (i+1, j)=(i, j)+(i, v).times..DELTA.t
Assuming that the vector 29 from point (j) to point (j-1) is represented by (i, j.fwdarw.j-1) at time t.sub.i, the vector 30 from point (j) to point (j+1) is (i, j.fwdarw.j+1), and the dimension of the vectors 29 and 30 are .vertline.i, j.fwdarw.j-1.vertline., .vertline.i, j.fwdarw.j+1.vertline., respectively, the direction of the deposition velocity 28 is, ##EQU1## Thus, the string is controlled by the above-described formula.
The simulation for etching is similarly executed on the basis of the String Model.
By the way, accompanying the fine patterning of recently developed semiconductor processes, it is necessary to predict the topography of an edge of an element, and a three-dimensional model is required. When the conventional String Model is extended to three dimensions the three-dimensional topography is represented by the surfaces of small triangles. However, to determine the movements of these triangles at every time interval .DELTA.t and to control the sizes and crossing of the surfaces makes the programming complicated and the calculation time and the memory capacity required are tremendously large. Therefore, it is impossible to realize a three-dimensional simulator.